OPTICS

DR.RIGOL

REFRACTION ON A SPHERICAL SURFACE

 

REFRACTION ON A SPHERICAL SURFACE:

If we consider only the paraxial rays, when the light incident parallel to the principal axes is refracted on a spherical surface ( with radius of curvature R), it will intercept the principal axes in the focus.

The formula that relates the focus (f) of curvature with the radius of curvature of the surface is :

Focus 001

Pay attention to the fact that the value of h doesnt appear in the formula, that means, the point of interception is independent of the value of h. That is true, of course, only for paraxial rays. Now, it will be ease to find the formula that relates the object distance, the image distance,

the radius of curvature with the indexes of refraction n1 and n2.

Using

Refraction of light 001

Using the symbols defined in the graph, lets get the expression for the formula for the refraction:

 

Refreaction Formula A 001

 

And this is the final result :

Refraction Formula B 001

Which is the formula we find in the books.